PSI - Issue 52

Chenxu Jiang et al. / Procedia Structural Integrity 52 (2024) 63–71 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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shown in Fig. 1b. The sheaf structure of spherulites has been manifested to lead to material anisotropy, making it important to analyze the structure and further understand the mechanical behavior of semi-crystalline polymers.

Fig. 1 (a) Transmission electron microscope of sheaf structure in PE (Vaughan, 1992) (b) Optical micrographs of MDPE (Butler & Donald, 1997)

Some researchers have proposed models for analyzing the mechanical behavior of semi-crystalline polymers, including layered two-phase composite models (Lee, Parks, Ahzi, & Solids, 1993) and three-phase composite models (Sedighiamiri, Van Erp, Peters, Govaert, & Van Dommelen, 2010). These models have been used to study the viscoplastic deformation behavior of semi-crystalline polymers under different loading conditions, such as uniaxial loading (Nikolov et al., 2002) and cyclic loading (Van Dommelen et al., 2003b). In addition, the relationship between the mechanical properties of semi-crystalline polymers and their structures at different scales, from micro- to meso- to macroscopic levels, has been a focus of research (Van Dommelen, Parks, Boyce, Brekelmans, & Baaijens, 2003a), (Uchida, Tokuda, & Tada, 2010), and (Oktay & Gürses, 2015). These studies improve our understanding of the complex deformation behavior of semi-crystalline polymers. Nonetheless, the above research idealized spherulites as completely radially symmetric structures, ignoring the effects of sheaf structure on its mechanical properties. This study then proposes an anisotropic spherulite model to quantitatively investigate the anisotropic mechanical properties of semi-crystalline polymers. The proposed model integrates crystal plasticity theory and molecular chain network theory into a finite element model to describe the micro-deformation behaviors of single and multiple spherulites. Furthermore, to validate the feasibility of the model, the study showcases the effects of crystallinity on mechanical properties and compares it with the data presented in the references. Nomenclature

Bulk modulus Cauchy stress e Elastic deformation gradient τ Flow stress λ Locking stretch coefficient Normal vector to the slip plane p Plastic deformation gradient p Plastic deformation rate Rate sensitivity coefficient μ Shear modulus γ Shear strain γ̇ Shear strain rate τ Shear stress